Information Fusion Robust Estimation For Multi-sensor Singular Systems With Missing Observation

Singular systems can be used to describe more performance characteristics of dynamical systems,and it has been widely used in many fields such as biological systems,dynamical systems,and circuit systems.The problem of state estimation of singular systems has attracted the attention of scholars because of its wide application background.Most of the existing literature studies models whose parameters are known,but in the actual process the system has model as well as networked stochastic uncertainties.These uncertainties will potentially lead to filter divergence.In this paper,the study of robust estimation for information fusion of multi-sensor singular systems with missing measurement consists of the following aspects:First,for the single sensor singular system with missing measurement and uncorrelated and correlated noise,the singular system is transformed into a standard system with reduced-order states without missing measurement using singular value decomposition(SVD)method and virtual noise method when the system noise variance and the measurement noise variance are uncertain.For the obtained standard system,robust time-varying and steady-state Kalman predictors are obtained based on the Kalman filtering algorithm.Robustness is proved using the Lyapunov equation method,which is based on the principle of transforming the robust problem into a non-negative qualitative problem with Lyapunov equation solutions.For the singular system with missing measurement and colored noise,the original singular system is transformed into a standard system with augmented states without colored noise using the SVD method and the state augmentation method,and the state estimation is performed to obtain the timevarying Kalman predictor.Next,for the multisensor singular system with missing measurement and uncertain white noise variance,the original singular system is transformed into a standard system with reduced-order state using SVD method,de-randomization method,and virtual noise method.For the obtained standard system in the reduced-order state,the robust local Kalman filtering algorithm of the reduced-order subsystem is proposed to obtain the robust local time-varying Kalman filter of the original system and the actual filtered mutual coincidence error variance array.The distributed fused time-varying Kalman filter is proposed by matrix-weighted,by diagonal matrix-weighted,and by scalar-weighted fusion.The robustness of the local and global filters is demonstrated using the Lyapunov equation method.The proposed algorithm is verified by a simulation example of a twoloop circuit system to prove the correctness as well as the effectiveness of the results.Finally,for the multisensor singular control system with missing measurement and correlated noise,the original singular system is transformed into a standard system with uncertain virtual noise only using SVD and de-randomization methods when the system noise variance and measuerment noise variance are uncertain.For the obtained standard system,a robust time-varying Kalman estimator for the reduced-order subsystem,a deconvolution estimator for the process noise,a robust local time-varying Kalman estimator for the original state,and a realistic estimation of the mutual coincidence error variance array are obtained based on the Kalman filtering algorithm.The linear minimum variance distributed fusion time-varying Kalman estimator is obtained based on the optimal distribution fusion criterion with matrix,scalar and diagonal matrix weighting.Global robustness is demonstrated using Lyapunov equation method and non-negative definite matrix decomposition method.The proposed algorithm is verified by a simulation example of a mechanical system with two connected oscillators and a damper to prove the correctness as well as the validity of the results.